Flow drag in polydisperse systems

The flow drag in heterogeneous systems is calculated by summing the forces exerted by the fluid on the particles in the system. If the solid particles are of the same size and uniformly dispersed, the forces are equal to one another. If the grain population is polydisperse, the problem seems to be difficult and still unsolved. A method is proposed to calculate the effective hydrodynamic grain size, which except for the size distribution, takes into account the packing fraction of solids. The method deals with the artificial transformation of a given system into a dense system of permeable aggregates of the same fluid permeability, the calculation of the effective aggregate radius in the population, and the conversion back to the arrangement of impermeable particles, which becomes converted in this way into the relevant monodisperse system. The effective size is calculated from the moment of the order D-3 of the size distribution by volume, where D is the fractal dimension of aggregates, dependent in a known way on the packing fraction of impermeable particles. A very good agreement with experiment is presented. The obtained result is thus a useful tool to predict the kinetics of flow in polydisperse systems, both those composed of fractal permeable aggregates and non-aggregated, usually formed in the sludge filtration, expression and sedimentation.